Question 653424
let f be first number
let s be second number
let t be third number

The second of three number is 4 times the first number:
s = 4f

The third number is 5 less than the second:
t = s - 5

If the first number is doubled and decreased by the third number and the result is the same as 23 more than the second number:
2f - t = 23 + s

Now that we have 3 equations, we can solve for f, s, and t:

Input t = s - 5 into the third equation:

2f - (s - 5) = 23 + s

Now replace every s with 4f

2f - (4f - 5) = 23 + 4f

Simplify

2f - 4f + 5 = 23 + 4f
-2f + 5 = 23 + 4f

subract 4f from both sides

-2f + 5 - 4f = 23

-6f + 5 = 23

subtract 5 from both sides

-6f = 18

divide both sides by -6:

f = -3

since s = 4f, then s = 4(-3) = -12

since t = s - 5, then t = -12 - 5 = -17